Monte Carlo simulations are very fun to write and can be incredibly useful for solving ticky math problems. In this post we explore how to write six very useful Monte Carlo simulations in R to get you thinking about how to use them on your own.

There is an iconic probability problem in The Empire Strikes Back! Han Solo is told that navigating an asteroid field is extremely unlikely to be successful. However not only does he navigate the asteroid field successfully, but we know he will. Learn how we can use Bayesian Priors to reconcile C3POs frequentist views on probability with our natural reasoning.

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Kullback–Leibler divergence is a very useful way to measure the difference between two probability distributions. In this post we'll go over a simple example to help you better grasp this interesting tool from information theory.

People often discuss the idea of being "90% certain" or "99% sure that this is true", but how big is the difference between these two values? It turns out that the difference between these values is similiar to the difference between having $10 and $100 in your wallet.

We have looked at working with a variety of analytical priors, but how can you sample from a prior probability that is not so mathematically pleasant to work with? In this post we learn about Rejection Sampling as one method of solving this problem.

Why is Variance related to X squared? To understand this we need to understand Moments of a Random Variable. Read on to learn about the relationship between Variance, Moments of a Random Variable and Jensen's inequality.

Many people find the ideas of Expectation and Variance confusing. In part this is because the way we view these concepts changes as our understanding grows in sophistication. In this post we'll look at the way these definitions change from their basic High School intro to the view of Rigorous Probability Theory.

Learn about Discrete and Continuous probability distributions as well as the types of questions that they can both answers. This post also discusses the relationship between the Binomial and Beta distributions.

Monte Carlo simulations are very fun to write and can be incredibly useful for solving ticky math problems. In this post we explore how to write six very useful Monte Carlo simulations in R to get you thinking about how to use them on your own.

There is an iconic probability problem in The Empire Strikes Back! Han Solo is told that navigating an asteroid field is extremely unlikely to be successful. However not only does he navigate the asteroid field successfully, but we know he will. Learn how we can use Bayesian Priors to reconcile C3POs frequentist views on probability with our natural reasoning.

Euler's number (the mathematical constant e) shows up in a variety of unexpected places. One of them is in Probability. A common way of expressing probabilities is to say "there's a 1 in a million chance!". In this post we find out how that way of viewing probabilities eventually leads us to Euler's number.

In this post we look at Expectation and Variance in simple terms, but through a more sophistcated lens. It turns out that "advanced" definitions of these terms are also easier to understand and work with.